Field of Invention
Embodiments of the present disclosure generally relate to generation of three orthogonal waveforms. In particular, the present disclosure relates to generation of three orthogonal waveforms to be used in any circuit including but not limited to OFDM, QAM, among others where complex number algebra is used.
Description of the Related Art
The background description includes information that may be useful in understanding the present invention. It is not an admission that any of the information provided herein is prior art or relevant to the presently claimed invention, or that any publication specifically or implicitly referenced is prior art.
In any modulation scheme employing in-phase and quadrature-phase components, the transmitted modulation signal over a period of duration T may be represented by the expression M(t)=A*cos(2pi*t/T)+B*sin(2pi*t/T), or as a similar sum of an alternate pair of orthogonal waveforms. The period T is known as a symbol period, and 1/T is defined to be the frequency (baseband or passband) or baud rate, FB. Data is communicated by selecting during each symbol period one of a limited number of permissible (A, B) vectors or symbols. Various such quadrature modulation schemes differ in the number, N, of possible symbols and the relative values of the (A, B) vectors corresponding to each possible symbol. Generally, the number, N, of possible symbols is an integer power of 2. Each transmitted symbol then communicates a unique string of log2 N bits.
A signal constellation is a graphical representation of the possible symbols for a given modulation scheme. The horizontal and vertical axes correspond to the orthogonal components of the modulation signal. Each possible symbol is represented by a point at the position of its associated (A, B) coordinates. A 64 point QAM can for instance be represented as an array of 64 points. Since log2(64)=6, the choice of one particular symbol for transmission during a given symbol period communicates six bits of information. Typically, the bits of information communicated per dimension or axes are equal, which in this example is three bits per axes.
Many other signal constellations are possible. For example, other variants of QAM also have array signal constellations but with various numbers of points. For QPSK (quadrature phase shift key) modulation, the four points of the signal constellation are arranged in a circle having the origin as a center.
QAM transmissions consist of modulating two signals on orthogonal carriers (such as a sine and a cosine carrier) and combining them on the same transmission channel. Since the carriers are orthogonal, the receiver may recover the two transmitted signals by demodulating the incoming signal with identical sine and cosine carriers. This method of modulation allows twice as much data to be transmitted on a given channel as a standard Amplitude Modulation (AM) approach. In Quadrature Amplitude Modulation (QAM), the signal point is a complex number having a real component and an imaginary component, wherein the real component of the signal is transmitted through Cosine waveform, and the imaginary component is transmitted using Sine waveform, wherein Sine and Cosine are orthogonal waveforms.
Existing systems therefore allow variable use of four different symbol signal spaces having 8, 16, 32, and 64 transmit points (corresponding to 3, 4, 5 or 6 bits per symbol respectively). In an aspect, if the Sine waveform transmits n bits and Cosine waveform also transmits n bits, the total transmission takes place of 2n bits. In a 16 QAM, Sine wave can transmit 2 bits and Cosine waveform can transmit 2 bits, making it a total of 4 bits being transmitted in one unit of transmission time interval. Similarly, in a 64 QAM, Sine wave will transmit 3 bits and Cosine waveform will transmit 3 bits, making it a total of 6 bits that can be transmitted in one unit of transmission time interval. It may however be desired to send more bits per unit of transmission time interval, which in the current system is restricted to 2n by means of two available orthogonal waveforms.
All publications herein are incorporated by reference to the same extent as if each individual publication or patent application were specifically and individually indicated to be incorporated by reference. Where a definition or use of a term in an incorporated reference is inconsistent or contrary to the definition of that term provided herein, the definition of that term provided herein applies and the definition of that term in the reference does not apply.
In some embodiments, the numbers expressing quantities of ingredients, properties such as concentration, reaction conditions, and so forth, used to describe and claim certain embodiments of the invention are to be understood as being modified in some instances by the term “about.” Accordingly, in some embodiments, the numerical parameters set forth in the written description and attached claims are approximations that can vary depending upon the desired properties sought to be obtained by a particular embodiment. In some embodiments, the numerical parameters should be construed in light of the number of reported significant digits and by applying ordinary rounding techniques. Notwithstanding that the numerical ranges and parameters setting forth the broad scope of some embodiments of the invention are approximations, the numerical values set forth in the specific examples are reported as precisely as practicable. The numerical values presented in some embodiments of the invention may contain certain errors necessarily resulting from the standard deviation found in their respective testing measurements.
As used in the description herein and throughout the claims that follow, the meaning of “a,” “an,” and “the” includes plural reference unless the context clearly dictates otherwise. Also, as used in the description herein, the meaning of “in” includes “in” and “on” unless the context clearly dictates otherwise.
The recitation of ranges of values herein is merely intended to serve as a shorthand method of referring individually to each separate value falling within the range. Unless otherwise indicated herein, each individual value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g. “such as”) provided with respect to certain embodiments herein is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention otherwise claimed. No language in the specification should be construed as indicating any non-claimed element essential to the practice of the invention.